How to correctly generate a 3d histogram using num

Question

This is more of a general question about 3d histogram creation in python.

I have attempted to create a 3d histogram using the X and Y arrays in the following code

import matplotlib
import pylab
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.axes3d import Axes3D
from matplotlib import cm

def threedhist():
    X = [1, 3, 5, 8, 6, 7, 1, 2, 4, 5]
    Y = [3, 4, 3, 6, 5, 3, 1, 2, 3, 8]
    fig = pylab.figure()
    ax = Axes3D(fig)
    ax.hist([X, Y], bins=10, range=[[0, 10], [0, 10]])
    plt.xlabel('X')
    plt.ylabel('Y')
    plt.zlabel('Frequency')
    plt.title('Histogram')
    plt.show()

However, I am getting the following error

Traceback (most recent call last):
  File "<pyshell#0>", line 1, in <module>
    a3dhistogram()
  File "C:/Users/ckiser/Desktop/Projects/Tom/Python Files/threedhistogram.py", line 24, in a3dhistogram
    ax.hist([X, Y], bins=10, range=[[0, 10], [0, 10]])
  File "C:\Python27\lib\site-packages\matplotlib\axes.py", line 7668, in hist
    m, bins = np.histogram(x[i], bins, weights=w[i], **hist_kwargs)
  File "C:\Python27\lib\site-packages\numpy\lib\function_base.py", line 169, in histogram
    mn, mx = [mi+0.0 for mi in range]
TypeError: can only concatenate list (not "float") to list

I have tried the code with and without the "[" in the line ax.hist([X, Y], bins=10, range=[[0, 10], [0, 10]]) I have also tried the function from numpy without success H, xedges, yedges = np.histogram2d(x, y, bins = (10, 10)) Am I missing a step or a parameter? Any advice would be greatly appreciated.

Answer 1

I've added to @lxop's answer to allow for arbitrary size buckets:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x = np.array([0, 2, 5, 10, 2, 3, 5, 2, 8, 10, 11])
y = np.array([0, 2, 5, 10, 6, 4, 2, 2, 5, 10, 11])
# This example actually counts the number of unique elements.
binsOne = sorted(set(x))
binsTwo = sorted(set(y))
# Just change binsOne and binsTwo to lists.
hist, xedges, yedges = np.histogram2d(x, y, bins=[binsOne, binsTwo])

# The start of each bucket.
xpos, ypos = np.meshgrid(xedges[:-1], yedges[:-1])

xpos = xpos.flatten()
ypos = ypos.flatten()
zpos = np.zeros_like(xpos)

# The width of each bucket.
dx, dy = np.meshgrid(xedges[1:] - xedges[:-1], yedges[1:] - yedges[:-1])

dx = dx.flatten()
dy = dy.flatten()
dz = hist.flatten()

ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color='b', zsort='average')

Answer 2

Have a look at http://matplotlib.sourceforge.net/examples/mplot3d/hist3d_demo.html, this has a working example script.

I've improved the code at that link to be more of a histogram:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
x = [1, 3, 5, 8, 6, 7, 1, 2, 4, 5]
y = [3, 4, 3, 6, 5, 3, 1, 2, 3, 8]

hist, xedges, yedges = np.histogram2d(x, y, bins=(4,4))
xpos, ypos = np.meshgrid(xedges[:-1]+xedges[1:], yedges[:-1]+yedges[1:])

xpos = xpos.flatten()/2.
ypos = ypos.flatten()/2.
zpos = np.zeros_like (xpos)

dx = xedges [1] - xedges [0]
dy = yedges [1] - yedges [0]
dz = hist.flatten()

ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color='b', zsort='average')
plt.xlabel ("X")
plt.ylabel ("Y")

plt.show()

I'm not sure how to do it with Axes3D.hist ().

Answer 3

In this answer there is a solution for 2D and 3D Histograms of scattered points. The usage is simple:

points, sub = hist2d_scatter( radius, density, bins=4 )

points, sub = hist3d_scatter( temperature, density, radius, bins=4 )

Where sub is a matplotlib "Subplot" instance (3D or not) and pointscontains the points used for the scatter plot.

Answer 4

I posted this in a related thread about colored 3d bar plots, but I think it's also relevant here as I couldn't find a complete answer for what I needed in either thread. This code generates a histogram scatterplot for any sort of x-y data. The height represents the frequency of values in that bin. So, for example, if you had many data point where (x,y) = (20,20) it would be high and red. If you had few data points in the bin where (x,y) = (100,100) it would be low and blue.

Note: result will vary substantially depending on how much data you have and how many bins your choose for you histogram. Adjust accordingly!

xAmplitudes = #your data here
yAmplitudes = #your other data here

x = np.array(xAmplitudes)   #turn x,y data into numpy arrays
y = np.array(yAmplitudes)

fig = plt.figure()          #create a canvas, tell matplotlib it's 3d
ax = fig.add_subplot(111, projection='3d')

#make histogram stuff - set bins - I choose 20x20 because I have a lot of data
hist, xedges, yedges = np.histogram2d(x, y, bins=(20,20))
xpos, ypos = np.meshgrid(xedges[:-1]+xedges[1:], yedges[:-1]+yedges[1:])

xpos = xpos.flatten()/2.
ypos = ypos.flatten()/2.
zpos = np.zeros_like (xpos)

dx = xedges [1] - xedges [0]
dy = yedges [1] - yedges [0]
dz = hist.flatten()

cmap = cm.get_cmap('jet') # Get desired colormap - you can change this!
max_height = np.max(dz)   # get range of colorbars so we can normalize
min_height = np.min(dz)
# scale each z to [0,1], and get their rgb values
rgba = [cmap((k-min_height)/max_height) for k in dz] 

ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color=rgba, zsort='average')
plt.title("X vs. Y Amplitudes for ____ Data")
plt.xlabel("My X data source")
plt.ylabel("My Y data source")
plt.savefig("Your_title_goes_here")
plt.show()

The results for about 75k data points of mine are below. Note, you can drag and drop to different perspectives and may want to save multiple views for presentations, posterity.